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Which sets are removable for holomorphic functions?
Prove analyticity by Morera’s theorem

Let $f$ be a continuous complex-valued function on $\mathbb{C}$ such that it is analytic everywhere outside $[-a,a] \subset \mathbb{R}$. Show that it is in fact entire.

  • $\begingroup$ When you say strip, do you mean an actual strip $[-a+it,a+it]$, as $t\in\mathbb R$ varies, or you really want the subset $[-a,a]\subset\mathbb R$? $\endgroup$
    – M Turgeon
    Sep 26, 2012 at 16:02
  • $\begingroup$ The latter one. Sorry for any confusion! $\endgroup$
    – Char
    Sep 26, 2012 at 16:06
  • 6
    $\begingroup$ This has been answered several times already. Search for "Morera" and you'll find some answers. $\endgroup$
    – WimC
    Sep 26, 2012 at 16:19
  • 1
    $\begingroup$ Thanks! I can see how that could be used to solve this problem! $\endgroup$
    – Char
    Sep 26, 2012 at 16:28
  • $\begingroup$ I started to type an answer but @WimC was faster.(+1) $\endgroup$
    – vesszabo
    Sep 26, 2012 at 16:45


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